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Recent questions tagged vectoranalysis
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1
GATE EC 2021  Question: 1
The vector function $F\left ( r \right )=x\hat{i}+y\hat{j}$ is defined over a circular arc $C$ shown in the figure. The line integral of $\int _{C} F\left ( r \right ).dr$ is $\frac{1}{2}$ $\frac{1}{4}$ $\frac{1}{6}$ $\frac{1}{3}$
asked
Feb 20
in
Vector Analysis
by
Arjun
(
4.4k
points)

18
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gateec2021
vectoranalysis
vectorinplanes
0
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0
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2
GATE EC 2021  Question: 16
If the vectors $(1.0,\:1.0,\:2.0)$, $(7.0,\:3.0,\:x)$ and $(2.0,\:3.0,\:1.0)$ in $\mathbb{R}^{3}$ are linearly dependent, the value of $x$ is __________
asked
Feb 20
in
Vector Analysis
by
Arjun
(
4.4k
points)

13
views
gateec2021
numericalanswers
vectoranalysis
vectorinplanes
0
votes
0
answers
3
GATE EC 2021  Question: 17
Consider the vector field $F\:=\:a_{x}\left ( 4yc_{1}z \right )+a_y\left ( 4x + 2z\right )+a_{z}\left ( 2y +z\right )$ in a rectangular coordinate system $(x,y,z)$ with unit vectors $a_{x},\:a_{y}$ and $a_{z}$. If the field $F$ is irrotational (conservative), then the constant $c_{1}$ (in integer) is _________________
asked
Feb 20
in
Vector Analysis
by
Arjun
(
4.4k
points)

12
views
gateec2021
numericalanswers
vectoranalysis
vectorinplanes
0
votes
0
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4
GATE EC 2021  Question: 37
For a vector field $D=\rho\cos^{2}\:\varphi \:a_{\rho }+z^{2}\sin^{2}\:\varphi \:a_{\varphi }$ in a cylindrical coordinate system $\left ( \rho ,\varphi ,z \right )$ with unit vectors $a_{\rho },a_{\varphi }$ and $a_{z}$, the ... $\left ( \rho =3, 0\leq z\leq 2 \right )$ (rounded off to two decimal places) is ________________
asked
Feb 20
in
Vector Analysis
by
Arjun
(
4.4k
points)

13
views
gateec2021
numericalanswers
vectoranalysis
0
votes
0
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5
GATE ECE 2020  Question: 1
If $v_{1},v_{2}, \dots ,v_{6}$ are six vectors in $\mathbb{R}^{4}$ , which one of the following statements is $\text{FALSE}$? It is not necessary that these vectors span $\mathbb{R}^{4}$. These vectors are not linearly independent. Any four of these vectors form a basis ... $\mathbb{R}^{4}$ , then it forms a basis for $\mathbb{R}^{4}$.
asked
Feb 13, 2020
in
Vector Analysis
by
jothee
(
1.8k
points)

113
views
gate2020ec
vectoranalysis
+1
vote
0
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6
GATE ECE 2020  Question: 2
For a vector field $\overrightarrow{A}$, which one of the following is $\text{FALSE}$? $\overrightarrow{A}$ is solenoidal if $\triangledown \cdot \overrightarrow{A}=0.$ $\triangledown \times \overrightarrow{A}$ ...
asked
Feb 13, 2020
in
Vector Analysis
by
jothee
(
1.8k
points)

118
views
gate2020ec
vectoranalysis
0
votes
0
answers
7
GATE ECE 2020  Question: 24
The random variable $Y=\int_{\infty }^{\infty }W\left ( t \right )\phi \left ( t \right )dt, \text{ where } \phi \left ( t \right )=\begin{cases} 1; & 5\leq t\leq 7 &\\ 0; & \text{otherwise} \end{cases}$ and $W(t)$ is ... noise process with twosided power spectral density $S_{W}\left ( f \right )=3 W/Hz$, for all $f$. The variance of $Y$ is ________.
asked
Feb 13, 2020
in
Vector Analysis
by
jothee
(
1.8k
points)

33
views
gate2020ec
numericalanswers
vectoranalysis
gaussstheorem
0
votes
0
answers
8
GATE ECE 2016 Set 3  Question: 27
If the vectors $e_1=(1,0,2)$, $e_2=(0,1,0)$ and $e_3=(2,0,1)$ form an orthogonal basis of the threedimensional real space $\mathbb{R}^3$, then the vector $\textbf{u}=(4,3,3)\in \mathbb{R}^3 $ can be expressed as $\textbf{u}=$ ... \frac{2}{5}$e_1+3e_2+$\large\frac{11}{5}$e_3 \\$ $\textbf{u}=$\large\frac{2}{5}$e_1+3e_2$\large\frac{11}{5}$e_3$
asked
Mar 28, 2018
in
Vector Analysis
by
Milicevic3306
(
15.8k
points)

22
views
gate2016ec3
vectoranalysis
0
votes
0
answers
9
GATE ECE 2016 Set 3  Question: 28
A triangle in the $xy$plane is bounded by the straight lines $2x=3y, \: y=0$ and $x=3$. The volume above the triangle and under the plane $x+y+z=6$ is _______
asked
Mar 28, 2018
in
Vector Analysis
by
Milicevic3306
(
15.8k
points)

18
views
gate2016ec3
numericalanswers
vectoranalysis
vectorinplanes
0
votes
0
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10
GATE ECE 2016 Set 3  Question: 50
A voicegrade AWGN (additive white Gaussian noise) telephone channel has a bandwidth of $4.0\:kHz$ and twosided noise power spectral density ${\large\frac{\eta}{2}}=2.5\times10^{5}Watt\:per\:Hz$. If information at the rate ... transmitted over this channel with arbitrarily small bit error rate, then the minimum bitenergy $E_b$ (in mJ/bit) necessary is _______
asked
Mar 28, 2018
in
Vector Analysis
by
Milicevic3306
(
15.8k
points)

17
views
gate2016ec3
numericalanswers
vectoranalysis
gauss'stheorem
0
votes
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11
GATE ECE 2016 Set 2  Question: 5
Consider the timevarying vector $\textbf{I}=\hat{x}15\cos(\omega t)+\hat{y}5\sin(\omega t)$ in Cartesian coordinates, where $\omega> 0$ is a constant. When the vector magnitude $\mid \textbf{I} \mid$ is at its minimum value, the angle $\theta$ that $\textbf{I}$ makes with the $x$ axis (in degrees, such that $ 0\leq \theta \leq 180)$ ________
asked
Mar 28, 2018
in
Vector Analysis
by
Milicevic3306
(
15.8k
points)

46
views
gate2016ec2
numericalanswers
vectoranalysis
0
votes
0
answers
12
GATE ECE 2016 Set 2  Question: 55
A positive charge $q$ is placed at $x=0$ between two infinte metal plates placed at $x=d$ and at $x=+d$ respectively. The metal plates lie in the $yz$ plane. The charge is at rest at $t=0$, when a voltage $+V$ is applied to the plate at $d$ and ... that the charge $q$ takes to reach the right plate is proportional to $d/V$ $\sqrt{d}/V$ $d/\sqrt{V}$ $\sqrt{d/V}$
asked
Mar 28, 2018
in
Vector Analysis
by
Milicevic3306
(
15.8k
points)

11
views
gate2016ec2
vectoranalysis
0
votes
0
answers
13
GATE ECE 2016 Set 1  Question: 29
The region specified by $\{ (\rho,\varphi,z):3 \leq\rho\leq 5,\frac{\pi}{8}\leq\varphi\leq\frac{\pi}{4}, \: 3\leq z\leq4.5\}$ in cylindrical coordinates has volume of _________
asked
Mar 28, 2018
in
Vector Analysis
by
Milicevic3306
(
15.8k
points)

23
views
gate2016ec1
numericalanswers
vectoranalysis
0
votes
0
answers
14
GATE ECE 2016 Set 1  Question: 50
An analog pulse $s(t)$ is transmitted over an additive white Gaussian noise (AWGN) channel. The received signal is $r(t) = s(t) + n(t)$, where $n(t)$ is additive white Gaussian noise with power spectral density $\frac{N_0}{2}$. The received signal is passed ... $E_s > E_h$ ; $SNR_{max}>\frac{2E_s}{N_0} \\ $ $E_s < E_h$ ; $SNR_{max}=\frac{2E_h}{N_0}$
asked
Mar 28, 2018
in
Vector Analysis
by
Milicevic3306
(
15.8k
points)

16
views
gate2016ec1
vectoranalysis
gauss'stheorem
0
votes
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answers
15
GATE ECE 2015 Set 3  Question: 3
If $C$ is a circle of radius $r$ with centre $z_{0},$ in the complex $z$plane and if $n$ is a nonzero integer, then $\oint _{C}\frac{dz}{(zz_{0})^{n+1}}$ equals $2\pi n j$ $0$ $\frac{nj}{2\pi}$ $2\pi n$
asked
Mar 28, 2018
in
Complex Analysis
by
Milicevic3306
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15.8k
points)

15
views
gate2015ec3
vectoranalysis
0
votes
0
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16
GATE ECE 2015 Set 3  Question: 4
Consider the function $g(t) = e^{t}\sin(2\pi t)u(t)$ where $u(t)$ is the unit step function. The area under $g(t)$ is ______.
asked
Mar 28, 2018
in
Vector Analysis
by
Milicevic3306
(
15.8k
points)

37
views
gate2015ec3
numericalanswers
vectoranalysis
0
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0
answers
17
GATE ECE 2015 Set 3  Question: 29
A vector field $\textbf{D} = 2\rho^{2}\:\textbf{a}_{\rho} + z\: \textbf{a}_{z}$ exists inside a cylindrical region enclosed by the surfaces $\rho =1,z = 0$ and $z = 5.$ Let $S$ be the surface bounding this cylindrical region. The surface integral of this field on $S(∯_{S} \textbf{D.ds})$ is _______.
asked
Mar 28, 2018
in
Vector Analysis
by
Milicevic3306
(
15.8k
points)

25
views
gate2015ec3
numericalanswers
vectoranalysis
0
votes
0
answers
18
GATE ECE 2015 Set 2  Question: 49
A zero mean white Gaussian noise having power spectral density $\dfrac{N_{0}}{2}$ is passed through an LTI filter whose impulse response $h(t)$ is shown in the figure. The variance of the filtered noise at $t = 4$ is $\dfrac{3}{2}A^{2}N_{0} \\$ $\dfrac{3}{4}A^{2}N_{0} \\$ $A^{2}N_{0} \\$ $\dfrac{1}{2}A^{2}N_{0}$
asked
Mar 28, 2018
in
Vector Analysis
by
Milicevic3306
(
15.8k
points)

15
views
gate2015ec2
vectoranalysis
gauss'stheorem
0
votes
0
answers
19
GATE ECE 2015 Set 1  Question: 25
A vector $\overrightarrow{P}$ is given by $\overrightarrow{P} = x^3y\overrightarrow{a}_x  x^2y^2\overrightarrow{a}_y  x^2 yz \overrightarrow{a}_z$. Which one of the statements is TRUE? $\overrightarrow{P}$ is ... irrotational, but not solenoidal $\overrightarrow{P}$ is neither solenoidal, nor irrotational $\overrightarrow{P}$ is both solenoidal and irrotational
asked
Mar 28, 2018
in
Vector Analysis
by
Milicevic3306
(
15.8k
points)

21
views
gate2015ec1
vectoranalysis
0
votes
0
answers
20
GATE ECE 2015 Set 1  Question: 54
The electric field intensity of a plane wave traveling in free space is given by the following expression $\textbf{E}(x,t)=\textbf{a}_y \: 24 \: \pi \: \: \cos(\omega t  k_0 x) \: \: (V/m)$ ... $x+y=1$. The total timeaveraged power (in mW) passing through the square area is _____________.
asked
Mar 28, 2018
in
Vector Analysis
by
Milicevic3306
(
15.8k
points)

11
views
gate2015ec1
numericalanswers
vectoranalysis
0
votes
0
answers
21
GATE ECE 2015 Set 1  Question: 55
Consider a uniform plane wave with amplitude $(E_0)$ of $10 \: V/m$ and $1.1$ GHz frequency travelling in air, and incident normally on a dielectric medium with complex relative permittivity $(\varepsilon _r)$ ... electric field component (in V/m) after it has travelled a distance of $10$ cm inside the dielectric region is ____________.
asked
Mar 28, 2018
in
Vector Analysis
by
Milicevic3306
(
15.8k
points)

15
views
gate2015ec1
numericalanswers
vectoranalysis
0
votes
0
answers
22
GATE ECE 2014 Set 4  Question: 2
The magnitude of the gradient for the function $f(x,y,z) = x^2 +3y^2 +z^3$ at the point $(1,1,1)$ is ___________.
asked
Mar 26, 2018
in
Vector Analysis
by
Milicevic3306
(
15.8k
points)

11
views
gate2014ec4
numericalanswers
vectoranalysis
gradient
0
votes
0
answers
23
GATE ECE 2014 Set 4  Question: 3
Let $X$ be a zero mean unit variance Gaussian random variable. $E[ \mid X \mid ]$ is equal to __________
asked
Mar 26, 2018
in
Vector Analysis
by
Milicevic3306
(
15.8k
points)

15
views
gate2014ec4
numericalanswers
vectoranalysis
gaussstheorem
randomvariable
0
votes
0
answers
24
GATE ECE 2014 Set 4  Question: 5
The directional derivative of $f(x,y)= \frac{xy}{\sqrt{2}} (x+y)$ at $(1,1)$ in the direction of the unit vector at an angle of $\frac{\pi}{4}$ with $y$axis, is given by _________.
asked
Mar 26, 2018
in
Vector Analysis
by
Milicevic3306
(
15.8k
points)

12
views
gate2014ec4
vectoranalysis
numericalanswers
0
votes
0
answers
25
GATE ECE 2014 Set 4  Question: 22
If calls arrive at a telephone exchange such that the time of arrival of any call is independent of the time of arrival of earlier or future calls, the probability distribution function of the total number of calls in a fixed time interval will be Poisson Gaussian Exponential Gamma
asked
Mar 26, 2018
in
Vector Analysis
by
Milicevic3306
(
15.8k
points)

19
views
gate2014ec4
vectoranalysis
gauss'stheorem
0
votes
0
answers
26
GATE ECE 2014 Set 4  Question: 49
Consider a communication scheme where the binary valued signal $X$ satisfies $P\{X=+1\}=0.75$ and $P\{X=1 \}=0.25$. The received signal $Y=X+Z$, where $Z$ is a Gaussian random variable with zero mean and variance ... $\sigma ^2$
asked
Mar 26, 2018
in
Vector Analysis
by
Milicevic3306
(
15.8k
points)

9
views
gate2014ec4
vectoranalysis
gauss'stheorem
0
votes
0
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27
GATE ECE 2014 Set 4  Question: 52
Consider a discretetime channel $Y=X +Z$, where the additive noise $Z$ is signaldependent. In particular, given the transmitted symbol $ X \in \{a , +a\}$ at any instant, the noise sample $Z$ is chosen independently from a Gaussian distribution with mean $\beta X$ and unit ... $\beta = 0.3$, the BER is closest to $10^{7}$ $10^{6}$ $10^{4}$ $10^{2}$
asked
Mar 26, 2018
in
Vector Analysis
by
Milicevic3306
(
15.8k
points)

11
views
gate2014ec4
vectoranalysis
gaussstheorem
0
votes
0
answers
28
GATE ECE 2014 Set 4  Question: 54
Gven $\overrightarrow{F} = z \hat{a}_x + x \hat{a}_y + y \hat{a}_z$. If $S$ represents the portion of the sphere $x^2 +y^2+z^2=1$ for $z \geq 0$, then $\int _s \nabla \times \overrightarrow{F} \cdot \overrightarrow{ds}$ is __________.
asked
Mar 26, 2018
in
Vector Analysis
by
Milicevic3306
(
15.8k
points)

13
views
gate2014ec4
numericalanswers
vectoranalysis
0
votes
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29
GATE ECE 2014 Set 3  Question: 53
Given the vector $\textbf{A}= ( \cos x ) ( \sin y )\hat{a_{x}}+( \sin x )( \cos y )\hat{a_{y}},$ where $\hat{a_{x}},$ $\hat{a_{y}}$ denote unit vectors along $x$, $y$ directions, respectively. The magnitude of curl of $\textbf{A}$ is __________
asked
Mar 26, 2018
in
Vector Analysis
by
Milicevic3306
(
15.8k
points)

22
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gate2014ec3
numericalanswers
vectoranalysis
0
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30
GATE ECE 2014 Set 2  Question: 22
The capacity of a bandlimited additive white Gaussian noise (AWGN) channel is given by $C = W \log_{2}\left ( 1+\frac{p} {\sigma ^{2}w} \right )$ bits per second (bps), where $W$ is the channel bandwidth, $P$ is the average power received ... channel capacity (in kbps) with infinite bandwidth $(W\rightarrow \infty )$ is approximately $1.44$ $1.08$ $0.72$ $0.36$
asked
Mar 26, 2018
in
Vector Analysis
by
Milicevic3306
(
15.8k
points)

40
views
gate2014ec2
vectoranalysis
gauss'stheorem
0
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0
answers
31
GATE ECE 2014 Set 2  Question: 29
If $\overrightarrow {r}= x\hat{a_{x}}+y\hat{a_{y}}+z\hat{a_{z}}$ and $\mid \overrightarrow{r} \mid= r$ , then $\text{div} ( r^{2} \nabla ( \text{ln }r ) )$ = _______ .
asked
Mar 26, 2018
in
Vector Analysis
by
Milicevic3306
(
15.8k
points)

20
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gate2014ec2
vectoranalysis
numericalanswers
0
votes
0
answers
32
GATE ECE 2014 Set 1  Question: 28
The volume under the surface $z(x,y) = x + y$ and above the triangle in the $x – y$ plane defined by $\{0 \leq y \leq x \: \text{and} \: 0 \leq x \leq 12\}$ is _______.
asked
Mar 26, 2018
in
Vector Analysis
by
Milicevic3306
(
15.8k
points)

24
views
gate2014ec1
numericalanswers
vectoranalysis
0
votes
0
answers
33
GATE ECE 2014 Set 1  Question: 46
Consider the state space model of a system, as given below ... The system is controllable and observable uncontrollable and observable uncontrollable and unobservable controllable and unobservable
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Mar 26, 2018
in
Vector Analysis
by
Milicevic3306
(
15.8k
points)

17
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gate2014ec1
vectoranalysis
0
votes
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34
GATE ECE 2014 Set 1  Question: 53
In spherical coordinates, let $\hat{a_{\theta}},\hat{a_{\phi}}$ denote unit vectors along the $\theta,\phi$ directions. $\textbf{E} = \dfrac{100}{r}\sin\theta \cos (\omega t  \beta r)\hat{a_{\theta}}\: V/m$ ... free space. The average power $(W)$ crossing the hemispherical shell located at $r = 1\:km,0\leq \theta \leq \pi/2$ is ______.
asked
Mar 26, 2018
in
Vector Analysis
by
Milicevic3306
(
15.8k
points)

34
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gate2014ec1
numericalanswers
vectoranalysis
0
votes
0
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35
GATE ECE 2013  Question: 53
A monochromatic plane wave of wavelength $\lambda = 600 \mu m$ is propagating in the direction as shown in the figure below. $\vec{E_{i}},\vec{E_{r}},$ and $\vec{E_{t}}$ ...
asked
Mar 26, 2018
in
Vector Analysis
by
Milicevic3306
(
15.8k
points)

21
views
gate2013ec
vectoranalysis
0
votes
0
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36
GATE ECE 2013  Question: 52
A monochromatic plane wave of wavelength $\lambda = 600 \mu m$ is propagating in the direction as shown in the figure below. $\vec{E_{i}},\vec{E_{r}},$ and $\vec{E_{t}}$ ...
asked
Mar 26, 2018
in
Vector Analysis
by
Milicevic3306
(
15.8k
points)

21
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gate2013ec
vectoranalysis
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votes
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37
GATE ECE 2013  Question: 39
The $\text{DFT}$ of a vector $\begin{bmatrix} a & b & c & d \end{bmatrix}$ is the vector $\begin{bmatrix} \alpha & \beta & \gamma & \delta \end{bmatrix}.$ ... $\begin{bmatrix} \alpha & \beta & \gamma & \delta \end{bmatrix}$
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Mar 26, 2018
in
Vector Analysis
by
Milicevic3306
(
15.8k
points)

14
views
gate2013ec
vectoranalysis
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votes
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answers
38
GATE ECE 2013  Question: 7
The divergence of the vector field $\overrightarrow{A} = x\hat{a}_{x} + y\hat{a}_{y} + z\hat{a}_{z}$ is $0$ $1/3$ $1$ $3$
asked
Mar 26, 2018
in
Vector Analysis
by
Milicevic3306
(
15.8k
points)

14
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gate2013ec
vectoranalysis
0
votes
0
answers
39
GATE ECE 2013  Question: 2
Consider a vector field $\vec{A}(\vec{r}).$ The closed loop line integral $\displaystyle {} \int \vec{A}\bullet\vec{dl}$ can be expressed as $\displaystyle {} \iint (\triangledown \times \vec{A}) \bullet\vec{ds}$ over the closed surface ... by the loop $\displaystyle {} \iiint (\triangledown \times \vec{A}) \bullet\vec{ds}$ over the open surface bounded by the loop
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Mar 26, 2018
in
Vector Analysis
by
Milicevic3306
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15.8k
points)

14
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gate2013ec
vectoranalysis
0
votes
0
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40
GATE ECE 2012  Question: 35
The direction of vector $A$ is radially outward from the origin, with $A=kr^n$ where $r^2=x^2+y^2+z^2$ and $k$ is a constant. The value of $n$ for which $\triangledown.A=0$ is $2$ $2$ $1$ $0$
asked
Mar 25, 2018
in
Vector Analysis
by
Milicevic3306
(
15.8k
points)

33
views
gate2012ec
vectoranalysis
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